Antenna Efficiency Calculator
Output
About Antenna Efficiency Calculator
The Antenna Efficiency Calculator estimates the aperture efficiency of a parabolic antenna based on its gain, physical aperture area, and operating wavelength.
This is crucial for understanding how effectively an antenna converts its physical aperture into an effective aperture for signal reception or transmission.
Formula
The effective aperture (Ae) of an antenna is given by:
$$ A_e = \frac{G \lambda^2}{4\pi} $$
The antenna aperture efficiency (eA) is the ratio of the effective aperture to the physical aperture area (A):
$$ e_A = \frac{A_e}{A} = \frac{G \lambda^2}{4\pi A} $$
Where:
- G: Antenna Gain (as a linear ratio). If given in dB, convert it using: $$ G = 10^{(G_{dB}/10)} $$.
- λ: Wavelength in meters (converted from nm, µm, or Å if necessary).
- A: Physical Aperture Area in m².
- eA: Antenna Aperture Efficiency (a dimensionless ratio).
Example Calculations
Example 1
- Antenna Gain (G): 100 (ratio)
- Physical Aperture Area (A): 0.5 m²
- Wavelength (λ): 600 nm = 600 × 10-9 m
Using the formula:
$$ A_e = \frac{100 \times (600 \times 10^{-9})^2}{4\pi} $$
This yields an effective aperture of approximately 2.87 × 10-12 m².
Thus, the antenna efficiency is:
$$ e_A = \frac{2.87 \times 10^{-12}}{0.5} \approx 5.74 \times 10^{-12} $$
Example 2
- Antenna Gain (G): 20 dB (converts to a linear gain of 100)
- Physical Aperture Area (A): 0.2 m²
- Wavelength (λ): 500 nm = 500 × 10-9 m
First, convert the gain:
$$ G = 10^{(20/10)} = 100 $$
Then, using the formula:
$$ A_e = \frac{100 \times (500 \times 10^{-9})^2}{4\pi} $$
The effective aperture is approximately 1.99 × 10-12 m², so:
$$ e_A = \frac{1.99 \times 10^{-12}}{0.2} \approx 9.95 \times 10^{-12} $$
Example 3
- Antenna Gain (G): 30 (ratio)
- Physical Aperture Area (A): 0.8 m²
- Wavelength (λ): 0.5 µm = 0.5 × 10-6 m
Using the formula:
$$ A_e = \frac{30 \times (0.5 \times 10^{-6})^2}{4\pi} $$
This results in an effective aperture of approximately 5.96 × 10-13 m², so the efficiency is:
$$ e_A = \frac{5.96 \times 10^{-13}}{0.8} \approx 7.45 \times 10^{-13} $$